I would simply not mention it for a while to start off. Forcing the issue will only cause them to dig in. When you think it's a good time to talk about it, ask them why they don't like the idea of you being armed. Get their reasons; your parents certainly give them weight so even if it's the same stuff you hear from antis all the time, discuss it intelligently. Then state your own position, and give the reasons why you carry concealed. Mention cases in the news, and also point out that the police have no duty to be security guards, and the time between you dialing 911 and help arriving can be several minutes, more than enough time for a bad guy to have done his evil deeds and left the scene.
It may not work; you may not get very far in the conversation. However you are an intelligent person (or so I gather from our many discourses here, friendly and otherwise
) so I have to assume you come from similar stock and that your parents will at least hear you out if you don't manage to convince them. Most hoplophobes eventually get over it once the lack of evidence to support their fear becomes telling.